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Hostpoco.com is offering a wordpress hosting service at a very affordable cost. our WordPress hosting Start from \$0.5 per month along with a single click script installer where you can install WordPress in a single click also can take backups and can finish the upgrade part. we offer totally managed website hosting plans. All WordPress/Application hosting plans comes no limit for resources and will be the perfect choice for high-traffic blogs or sites.

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## complexity theory – Padding in proof of space hierarchy theorems

Suppose that we consider instead the language
$$L = { langle M rangle : text{M does not accept langle M rangle in space f(langle M rangle)} }.$$
We want to show that $$L notin mathsf{SPACE}(o(f(n))$$, that is, that if $$M$$ uses space $$o(f(n))$$ then $$L(M) neq L$$. This should be the case since $$langle M rangle in L Leftrightarrow langle M rangle notin L(M).$$
But is this really true? According to the definition of $$L$$, $$langle M rangle in L$$ iff $$M$$ does not accept $$langle M rangle$$ in space $$f(langle M rangle)$$. It could be that $$langle M rangle in L$$ and $$M$$ accepts $$langle M rangle$$ using more than $$f(langle M rangle)$$ space. The latter could actually happen, since we are only guaranteed that $$M$$ uses space $$g(n)$$ for some function $$g(n) = o(f(n))$$, which does not preclude $$g(|langle M rangle|) > f(|langle M rangle|)$$ at the particular value $$|langle M rangle|$$.

Adding the padding fixes this issue: it cannot be that $$g(|(langle M rangle, 10^k)|) > f(|(langle M rangle, 10^k)|)$$ for all $$k$$, since this would contradict $$g(n) = o(f(n))$$.

## html – creates an unnecessary space in content?

So by default WordPress include `<p></p>` into the content.

My view source output:

``````<td class="ccontent">
<p>I would suggest choosing an easier method,<br />
This one is pretty difficult one.</p>
<p>Just a thought.</p>
</td>
``````

On my website:

As you can see there’s a weird space at the bottom.

When I include `<?php the_title();?>` it aligns great.

But when I include `<?php the_content();?>` the space appears.

I did an experiment and removed the `<p>` from the content (using function filter).

Then it aligns great, but the content shows in a single line (which I don’t want).

So I figured that `<p></p>` is causing this problem.

Is there any way to fix this?

Desperatly need help.

## general topology – A \$sigma\$-compact but not hemicompact space?

All spaces are at least Hausdorff. A topological space $$X$$ is called

• $$sigma$$-compact if there is a countable sequence $$(K_n)_{n of compact subsets of $$X$$ such that $$X=bigcup_n K_n$$.
• hemicompact if there is a countable sequence $$(K_n)_{n of compact subsets of $$X$$ such that for every $$Ksubseteq X$$ compact there is $$ninomega$$ with $$Ksubseteq K_n$$.

In particular a hemicompact $$T_1$$-space $$X$$ is $$sigma$$-compact since for every $$xin X$$ there is $$n$$ with $${x}subseteq K_n$$, hence $$X=bigcup_n K_n$$. I’m interested in conditions on $$X$$ that are sufficient to reverse this implication, but I am more interested in an example of a space $$X$$ (with $$X$$ at least Hausdorff, better if completely regular) which is $$sigma$$-compact but not hemicompact. I have checked the standard sources (Counterexamples in Topology and the pi-base website) but there are no examples of such spaces there, hence my question:

What is an example of an Hausdorff space $$X$$ which is $$sigma$$-compact but not hemicompact?

## backup – How to back-up a folder every 15 minutes without taking up more space than needed?

I’m incrementally backing up my coding project with Duplicity and am finding it’s consuming storage faster than expected.

The folder I’m backing up consists mostly of gifs, images, and libraries that take up most of the space and are only occasionally changed, and my script files which take up very little space but need to be backed up every 15 minutes or so to avoid losing hours of progress if data is accidentally deleted.

Since Duplicity doesn’t store the files whole but has encrypted slices that need to be restored, I assumed that means it’s only copying the parts of the folders that need to be changed into a snapshot and algorithmically piecing it together?

If not, is there a tool that would be more efficient for doing this? Ideally I’m trying to set up a system that backs up the entire folder to a USB drive once per day, and does a more efficient sync every 15 minutes so I can easily go back if I accidentally delete everything.

## algebraic number theory – non-Archimedean normed space

Definition Let $$(F,|cdot|)$$ be a field equipped with an absolute value. A normed vector space over $$F$$ is a pair $$(V,|cdot|)$$ consisting of an $$F$$-vector space $$V$$ and a map $$|cdot| : V → mathbb{R}$$ satisfying

• $$|v|geq 0$$ with equality if and only if $$v = 0$$,
• $$|cv| = |c|cdot|v|$$ for all $$cin F$$ and $$vin V$$,
• $$|v + w| leq |v| + |w|$$ for all $$v,w in V$$.

How to prove that if $$F$$ is non-archimedean then there is a constant $$C > 0$$ (depending on the normed vector space) such that $$|v+w| leq Cmax(|v|,|w|)$$ for all $$v,w in V$$.

## internal storage – How do I get rid of broken, invisible files that take up lots of space?

I tried downloading a pretty big mp4 file, but that failed because i didn’t have enough space.

However, it filled up all my leftover storage. I tried getting rid of it but it doesn’t show up in the file explorer. I checked hidden files.

Checking device care -> storage, it seems like it’s in the “other” category.

I’m kinda desperate because i need the storage space to work. How do i clear it up?

Samsung galaxy Tab S4, Amdroid 10

## mac – Is it okay to create space on APFS synthesized disk to install windows without bootcamp?

Honestly I do not have enough reputation to comment on this post:

https://apple.stackexchange.com/a/307469/425311

Step two in the above link says:

Create empty space on a drive. This space needs to be outside any APFS or Core Storage containers.

His command `diskutil list` shows:

``````/dev/disk0 (internal, physical):
#:                       TYPE NAME                    SIZE       IDENTIFIER
0:      GUID_partition_scheme                        *536.9 GB   disk0
1:                        EFI EFI                     209.7 MB   disk0s1
2:                  Apple_HFS Chicken                 150.0 GB   disk0s2
3:                 Apple_Boot Recovery HD             650.0 MB   disk0s3
4:                  Apple_HFS Turkey                  150.0 GB   disk0s4
5:                 Apple_Boot Recovery HD             650.0 MB   disk0s5
``````

Mine shows:

``````/dev/disk0 (internal, physical):
#:                       TYPE NAME                    SIZE       IDENTIFIER
0:      GUID_partition_scheme                        *240.1 GB   disk0
1:                        EFI EFI                     209.7 MB   disk0s1
2:                 Apple_APFS Container disk1         239.8 GB   disk0s2

/dev/disk1 (synthesized):
#:                       TYPE NAME                    SIZE       IDENTIFIER
0:      APFS Container Scheme -                      +239.8 GB   disk1
Physical Store disk0s2
1:                APFS Volume JacOS                   40.2 GB    disk1s1
2:                APFS Volume Preboot                 22.5 MB    disk1s2
3:                APFS Volume Recovery                512.1 MB   disk1s3
4:                APFS Volume VM                      2.1 GB     disk1s4
``````

Continuing with the instruction will “absorb the free space” into a volume which is on an APFS container scheme, which is opposite of the instruction in step two because my volumes are on a synthesized APFS container scheme.

Does it matter that my volumes to “absorb the free space” is on a scheme and not a container disk?

I’m hesitant to experiment with container disks which contain the only OS.

Also, in step three, why does David resize disk1s4 instead of disk0s4?

Has that created the below result, which causes the identifier to reflect the number “1” after disk, even though it is reading off the internal physical disk “disk0”?

``````/dev/disk0 (internal, physical):
#:                       TYPE NAME                    SIZE       IDENTIFIER
0:      GUID_partition_scheme                        +536.9 GB   disk1
1:                        EFI EFI                     209.7 MB   disk1s1
2:                  Apple_HFS Chicken                 150.0 GB   disk1s2
3:                 Apple_Boot Recovery HD             650.0 MB   disk1s3
4:                  Apple_HFS Turkey                  385.4 GB   disk1s4
5:                 Apple_Boot Recovery HD             650.0 MB   disk1s6
``````

Does David create a virtual partition when resizing a volume by changing the numeral of the internal physical disk?
Am I to add a numeral to my “disk1s3” (the second to last volume in my container scheme) to be “disk2s3”?

I don’t understand and am I not sure how to proceed with the instructions.